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            Bongiovanni, Eliot; Di Giosia, Leonardo; Diaz, Alejandro; Habib, Jahangir; Kakkar, Arjun; Kenigsberg, Lea; Pittman, Dylanger; Sothanaphan, Nat; Zhu, Weitao (, Analysis and Geometry in Metric Spaces)Abstract The classic double bubble theorem says that the least-perimeter way to enclose and separate two prescribed volumes in ℝ N is the standard double bubble. We seek the optimal double bubble in ℝ N with density, which we assume to be strictly log-convex. For N = 1 we show that the solution is sometimes two contiguous intervals and sometimes three contiguous intervals. In higher dimensions we think that the solution is sometimes a standard double bubble and sometimes concentric spheres (e.g. for one volume small and the other large).more » « less
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